This study is designed to determine if an antibody (CC49) which has been labeled with the radionuclide (131) and injected into a vein, will bind primarily to tumors but not to normal tissues, allowing detection of these tumors by scanning and a therapeutic delivery of radiation. This radiolabeled antibody, 131I-CC49, is an investigational agent. The amount of radioactivity bound to the antibody is larger than that used for diagnostic scanning in hopes that therapeutic doses of radiation can be selectively delivered to the tumor sites. The 131I-antibody will be injected once, as one treatment course. Interferon, an agent to stimulate cells to express the substance that the CC49 antibody reacts with, will be given before and after the antibody. This study is open to patients with adenocarcinoma of the prostate. Prior to entry into the study, blood will be tested for the presence of human immunodeficiency virus antibody and hepatitis B surface antigen. Two days prior to receiving the antibody (and continuing daily for two weeks thereafter), patients will receive a Lugol's iodine solution that will help keep the radioactive iodine from going to the thyroid; a thyroid hormone pill to suppress the thyroid will also be used. On the day of antibody infusion, patients will be given a dose of non-radioactive antibody and observed for allergic reaction. If there is allergic reaction, patients will not go on this study. After the radioactive antibody has been injected, patients will be required to stay in the hospital room until the amount of radioactivity decreases to a level which will not expose other people to significant risk (approximately 5 days). Toxicity and response will be monitored by laboratory and clinical criteria with the addition of radiographic evaluation when appropriate.